The second desirable consequence is such: since the game \(\mathcal {G}\)  has the \((\mathcal {V}^{*}, \mathcal {W}^{*})\) -subjective \(\epsilon \) -satisficing paths property within \(\mathbf {\Pi }\) , play can be driven to (subjective) \(\epsilon \) -equilibrium by changing only the policies of those players that are “\(\epsilon \) -unsatisfied," so to speak. We thus obtain a stopping condition, whereby player \(i\)  can settle on a policy whenever it is subjectively \(\epsilon \) -best-responding. In contrast, the stability of \(\epsilon \) -equilibrium may be threatened when an algorithm requires a player to change policies while already \(\epsilon \) -best-responding. We selectively cite [1]}, [2]} and [3]} as recent examples of work showing non-convergence of policies to equilibrium when each agent runs a policy gradient algorithm.
